Professor-Fortune-Massamba

Professor Fortuné Massamba

On Some Geometric Structures in Smooth Manifolds

Abstract

The contact and almost contact structures are two of the most interesting examples of differential geometric structures. Their theory is a natural generalization of so-called contact geometry, which has important applications in classical and quantum mechanics.  Almost contact metric structures are an odd-dimensional analogue of almost Hermitian structures and there exist many important connections between these two classes. In this lecture, we pay attention to some specific structures, namely, Sasakian, Kenmotsu, cosymplectic and symplectic structures. Among other results, we prove that there exist leaves of some distributions of null hypersurfaces in indefinite Sasakian settings which are extrinsic spheres.  We also show that,  there are foliations on almost Weyl null hypersufaces which are Einstein-Weyl with scalar curvature of constant sign. A solution of the Goldberg conjecture by Sekigawa is that there exists no Einstein metric with non-negative Ricci curvature satisfying an invariant on compact symplectic manifolds that admit no Kahler structure.

Curriculum Vitae

Education

  • Docteur ès Sciences (Ph D): Mathematics, speciality: Differential Geometry, completed at the Institut de Mathématiques et de Sciences Physiques (IMSP), University of Abomey-Calavi, (Benin)/The Abdus Salam International Centre for Theoretical Physics (ICTP), 22 September 2004
  • Diplôme d’Etudes Approfondies (DEA): Advanced Postgraduate Diploma, speciality: Differential Geometry, IMSP (Benin), 16 December 1999
  • Attestation d’Etudes Approfondies (AEA): Advanced Postgraduate Certificate, speciality: Differential Geometry, Cheikh Anta Diop University of Dakar (Senegal), July 1998
  • Master’s degree in Pure Mathematics, Cheikh Anta Diop University of Dakar (Senegal), October 1997
  • Bachelor’s degree in Mathematics, Cheikh Anta Diop University of Dakar (Senegal), October 1996
  • University Diploma taken after two years’ study in Mathematics and Physics, Marien Ngouabi University of Brazzaville (Congo), June 1993

Professional experience

  • Full Professor in the School of Mathematics, Statistics and Computer Science (University of KwaZulu-Natal), from 01 Januray 2019 to date
  • Associate Professor in the School of Mathematics, Statistics and Computer Science (University of KwaZulu-Natal), from 30 May 2013 to 31 December 2018
  • Senior Lecturer in the Department of Mathematics (University of Botswana), from 26 November 2008 to 30 May 2013
  • Lecturer in the Department of Mathematics (University of Botswana), from 18 April 2006 to 26 November 2008
  • Postdoctoral position at the International Chair in Mathematical Physics and Applications (ICMPA)-UNESCO Chair (Abomey-Calavi University, Benin), from January 2005 to March 2006
  •  
  • Full Professor in the School of Mathematics, Statistics and Computer Science (University of KwaZulu-Natal), from 01 Januray 2019 to date
  • Associate Professor in the School of Mathematics, Statistics and Computer Science (University of KwaZulu-Natal), from 30 May 2013 to 31 December 2018Lecturer in Real Analysis I and II at the Institut Universitaire du Benin (Benin), from October 2004 to March 2005
  • Mathematics and Physics Teacher in Secondary School College Mansimou (Brazzaville), Congo, from 1993 to 1995

 

Supervision of higher degree

 

  • E. Gnandi (Togo), Some geometric aspects of locally conformal almost cosymplectic manifolds, IMSP (University of Abomey-Calavi, Benin), Msc completed in April 2019
  • A. Diallo (Guinea), Improved Chen-Ricci inequality for curvature-like tensors, IMSP (University of Abomey-Calavi, Benin), Msc completed in April 2019
  • B. Betolngar (Chad), MSc title: Geometry of warped product CR-submanifolds in Kähler manifolds, IMSP (University of Abomey-Calavi, Benin), Msc completed in April 2019
  • E. N. Lazarus (Namibia), MSc title: Locally conformal conformal Sasakian geometry, IMSP (University of Abomey-Calavi, Benin), Msc completed in March 2019
  • M. A. BOYE (Mauritania), MSc title: Isometric immersions of pseudo-Riemannian space forms, UKZN, Msc completed in December 2018
  • S. Ssekajja (Uganda), PhD title: Some investigations on null geometry and its applications, UKZN, PhD completed in September 2018
  • A. Attiogbe (Togo), Msc title: On some geometric aspects of doubly twisted product immersions, IMSP (Benin), MSc completed in December 2017
  • Miss S. H. Maduna (South Africa), BSc hons title: Basic Features of Symplectic Geometry, UKZN, BSc Hons completed November 2017
  • S. Longwap (Nigeria), PhD title: On some Riemannian submersions and affine Szabo manifolds, UKZN, PhD completed in November 2017
  • A. Maloko-Mavambou (Congo), PhD title: On the geometry of locally conformal almost cosymplectic manifolds and 2-order Lagrange space, UKZN, completed in October 2017
  • S. Ssekajja (Uganda), MSc title: On the null geometry of quasi Generalized CR-submanifolds of indefinite nearly α-Sasakian manifolds, University of KwaZulu-Natal, Msc completed in June 2016
  • L. Mazibuko (South Africa), Msc title: On the geometry of CR-submanifolds, UKZN, Msc completed in March 2016
  • P. R. Majozi (South Africa), Msc title: On Huppert conjecture for some quasi-simple groups, University of KwaZulu-Natal, Msc completed in March 2015
  • S. Mafunda (South Africa), BSc hons title: Frenet frame of curves and first fundamental form on surfaces, University of KwaZulu-Natal (UKZN), BSc Hons completed December 2014
  • J.-P. Tshikuna-Matamba (DR Congo), PhD title: The differential geometry of the fibres of almost contact metric submersions, University of South Africa (UNISA), completed in June 2014
  • Goitsemang (Botswana), BSc title: On Bilinear and Quadratic Form, University of Botswana, Bsc completed in Avril 2013
  • P. Moile (Botswana), MSc title: Symmetries in lightlike hypersurfaces of Kenmotsu manifolds, University of Botswana, MSc completed in June 2011
  • R. Motsopa (Botswana), BSc title: Curvature and Geodesic of the 2-torus, University of Botswana, Bsc completed in April 2007  

 

Referees

 

  • Augustin Banyaga: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA, E-mail : banyaga@math.psu.edu
  • Jean-Baptiste Gatsinzi: Department of Mathematics and Computional Sciences, Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana, E-mail : gatsinzij@biust.ac.bw

 

Workshop/ Conference attended

 

  • Groupes, géométrie et analyse, Conference in honor of Prof. Alain Valette, Institut des Hautes Etudes Scientifiques (IHES), 17-18 December 2018
  • Topology, Algebra, Analysis and Geometry (TAAG) Conference, University of KwaZulu-Natal, Durban, 17-19 September 2018
  • ICM2018, Rio de Janeiro (Brazil), 01 – 09 August 2018
  • GIRAGA Seminar XVI, IMSP, Dangbo (Benin), 17 – 22 December 2017
  • Topology, Algebra, Analysis and Geometry (TAAG) Conference, University of Botswana, Gaborone, 18-20 September 2017
  • The 4th Benin-Brazil Meeting on Mathematics and Physical Sciences in honor of Prof. A. Banyaga, Dangbo (Benin) 3-15 July 2017
  • 12th COPROMATH International School and Special International Conference in Mathematics in honor of Prof. M. N. Hounkonnou, 24 October 2016 – 04 November 2016, Cotonou, Benin
  • Conference on Topology, Algebra and Category Theory, 19-21 September 2016, UNISA, Johannesburg, South Africa
  • SAMS (South African Mathematical Society), 57th annual congress, 29-31 October 2014, UNISA, Johannesburg, South Africa
  • SAMSA and MASAMU project, 22-30 November 2013, Stellenbosch, South Africa
  • SAMS, 56th annual congress, 30 October – 01 November 2013, Pietermaritzburg, South Africa
  • Workshop on Geometric Analysis, 3-7 December 2012, Cape Town, South Africa
  • Conference on Topology, Algebra and Category Theory in memory of Sergio Salbany, 10-12 September 2012, Pretoria, South Africa
  • School and Conference in Geometric Analysis, ICTP, Trieste (Italy), from 11-29 June 2012
  • Algebra, Geometry and Topology Conference, University of Namibia, Windhoek (Namibia), 15-16 September 2011
  • Workshop on Combinatorial Methods in Algebraic Geometry and Commutative Algebra, Max-Planck Institute for Mathematics in the Sciences, Leipzig (Germany), 05-07 July 2011
  • Mini-Conference in Algebra, Geometry and Topology, University of Botswana, Gaborone (Botswana), 11 August 2010
  • School on Hodge Theory and related topics, ICTP, Trieste (Italy), from 14th June 2010 to 02 July 2010
  • Geometric Analysis and Riemannian Geometry in honor of Yuanlong Xin towards his 65th birthday, Max-Planck Institute for Mathematics in the Sciences, Leipzig (Germany), 23-24 July 2009
  • GIRAGA XII Seminar and Jean-Pierre Ezin Colloquium, Cotonou (Benin), 01-12 December 2008
  • Third International School and Fifth International Workshop on Contemporary Problems in Mathematical Physics, Cotonou (Benin), from 22 October to 02 November 2007
  • International School on the Geometry of Near Points, Symplectic Geometry and Applications, Marien Ngouabi University of Brazzaville (Congo), 17-27 January 2006

 

 

Refereed Journal Articles

 

 

  • Fortuné Massamba and S. Ssekajja, On total mean curvatures of foliated half-lightlike submanifolds in semi-Riemannian manifolds, Hacettepe Journal of Mathematics and Statistics, accepted 2019
  • Fortuné Massamba and S. Ssekajja, Null hypersurfaces evolved by their mean Curvature in a Lorentzian manifold, Colloquium Mathematicum, 157 (2019) , 83-106
  • H. A. Hamed, Fortuné Massamba and S. Ssekajja, On null submanifolds of generalized Robertson-Walker space forms, Turkish Journal of Mathematics, 43(2019), 1650-1667
  • S. Diallo, Fortuné Massamba and S. J. Mbatakou, Warped products with Tripathi connections, Afrika Matematika, 30 (2019), no. 3-4, 389-398
  • Fortuné Massamba and S. Ssekajja, Higher order mean curvatures of SAC half-lightlike submanifolds of indefinite almost contact manifolds, Revista de la Unión Matemática Argentina, 60 (2019), no. 1, 21-44
  • Fortuné Massamba and S. Ssekajja, Some integrations on null hypersurfaces in Lorentzian manifolds, Bulletin of the Korean Mathematical Society, 56 (2019), no. 1, 229-243
  • Fortuné Massamba, A note on curvatures and rank 2 Seiberg-Witten invariants, Mathematical Structures and Applications (Book Chapter), Springer Nature Switzerland AG 2018, 375-391
  • S. Diallo, S. Longwap and Fortuné Massamba, Almost Kähler eight-dimensional Walker manifold, Novi Sad Journal of Mathematics, 48 (2018), no. 1, 129-141
  • Fortuné Massamba and A. Maloko Mavambou, A class of locally conformal almost cosymplectic manifolds, Bulletin of the Malaysian Mathematical Sciences Society, 41 (2018), no. 2, 545-563
  • Banyaga, J.-B. Gatsinzi and Fortuné Massamba, A note on the formality of some contact manifolds, Journal of Geometry, 109 (2018), no. 1, Art. 3, 10 pp.
  • Fortuné Massamba and S. Ssekajja, Generalized Raychaudhuri’s equation for null hypersurfaces, Matematicki Vesnik, 70 (1) (2018), 79-88
  • Longwap and Fortuné Massamba, The geometry of tangent bundles and almost complex structures, Acta Matematica Academie Paedagogiace Nyı́regyháziensis, 33 (2017), 273-290
  • Fortuné Massamba and P. P. Ntumba, On sheaves of differential operators, Rendiconti dell’Istituto di Matemstica dell’Università di Trieste, 49 (2017), 357-365
  • Fortuné Massamba and S. Ssekajja, A new approach to totally umbilical null submanifolds, Novi Sad Journal of Mathematics, 47 (2) (2017), 63-76
  • Fortuné Massamba, A conformal connection on null hypersurfaces in indefinite Kenmotsu manifolds, Bulletin of the Malaysian Mathematical Sciences Society, 40 (4) (2017), 1559-1575
  • S. Diallo, S. Longwap and Fortuné Massamba, On twisted Riemannian extensions associated with Szabó metrics, Hacettepe Journal of Mathematics and Statistics, 46 (4) (2017), 593-601
  • Fortuné Massamba, A. Maloko Mavambou and S. Ssekajja, On Indefinite locally conformal cosymplectic manifolds, Communications of the Korean Mathematical Society, 32 (2017), No. 3, 725-743
  • Fortuné Massamba and S. J. Mbatakou, Induced and intrinsic Hashiguchi connections on Finsler submanifolds, Balkan Journal of Geometry and Its Applications, Vol.22 (2017), No.2, 50-62
  • S. Diallo, S. Longwap and Fortuné Massamba, On three dimensional affine Szabó manifolds, Balkan Journal of Geometry and Its Applications, Vol.22 (2017), No.2, 21-36
  • S. Diallo and Fortuné Massamba, Affine Szabó connections on smooth manifolds, Revista de la Unión Matemática Argentina, 58 (2017), No. 1, 37-52
  • Fortuné Massamba and S. Ssekajja, A note on quasi generalized CR-lightlike geometry in indefinite nearly μ-Sasakian manifold, International Journal of Geometric Methods in Modern Physics, (2017) no. 3, 1750045, 17 pp.
  • Fortuné Massamba, Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds, Mathematica Slovaca, 66 (2016), no. 6, 1443-1458
  • Fortuné Massamba and S. Ssekajja, Some remarks on quasi generalized CR-null geometry in indefinite nearly cosymplectic manifolds, International Journal of Mathematics and Mathematical Sciences, Vol. 2016 (2016), Article ID 9613182, 10 pp.
  • Lungiambudila, Fortuné Massamba and J. Tossa, Equivalence Conditions of Symmetry Properties in Lightlike Hypersurfaces of Indefinite Kenmotsu Manifolds, Bulletin of the Korean Mathematical Society, 53 (2016), No. 4, 1259-1280
  • Fortuné Massamba and S. Ssekajja, Quasi Generalized CR-lightlike Submanifolds of indefinite nearly Sasakian manifolds, Arabian Journal of Mathematics, 5(2016), No. 2, 87-101
  • Augustin Banyaga and Fortuné Massamba, Non-existence of certain Einstein metrics on some symmetric manifolds, Forum Mathematicum, 28 (2016), No. 3, 527-537
  • Fortuné Massamba and T. Tshituna-Matamba, Horizontally submersions of contact CR-submanifolds, Turkish Journal of Mathematics, 38 (2014), No. 3 436-453
  • Fortuné Massamba, Symmetries of null geometry in indefinite Kenmotsu manifolds, Mediterranean Journal of Mathematics, 10 (2013), No. 2, 1079-1100
  • Fortuné Massamba, Lighlike hypersurfaces in indefinite trans-Sasakian manifolds, Results in Mathematics, 63 (2013), No. 1, 251-287
  • Fortuné Massamba, Screen conformal invariant lightlike hypersurfaces of indefinite Sasakian space forms, African Diaspora Journal of Mathematics, 14 (2012), No 2, 22-37
  • Fortuné Massamba, Screen almost conformal lightlike geometry in indefinite Kenmotsu space forms, International Electronic Journal of Geometry, 5 (2012), no 2, 36-58
  • Fortuné Massamba, On lightlike geometry in indefinite Kenmotsu manifolds, Mathematica Slovaca, 62 (2012), No. 2, 315-344
  • Fortuné Massamba, Lightlike geometry of leaves in indefinite Kenmotsu manifolds, Cubo, 13 (2011), No. 3, 69-89
  • Fortuné Massamba, Relative nullity foliations and lightlike hypersurfaces of indefinite Kenmotsu manifolds, Turkish Journal of Mathematics, 35 (2011), No. 1, 129-149
  • Lungiambudila, Fortuné Massamba and J. Tossa, Symmetry properties of lightlike hypersurfaces of indefinite Sasakian manifolds, Science University Tokyo (SUT) Journal of Mathematics, 46 (2010), No. 2, 177-204
  • Fortuné Massamba, On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds, Journal of Geometry, 95 (2009), 73-89
  • Fortuné Massamba, Screen integrable lightlike hypersurfaces of indefinite Sasakian manifolds, Mediterranean Journal of Mathematics, 6 (2009), No. 1, 27-46
  • Fortuné Massamba, On weakly Ricci symmetric lightlike hypersurfaces of indefinite Sasakian manifolds, Science University Tokyo (SUT) Journal of Mathematics, 44 (2008), No. 2, 181-201
  • Ben Geloun, M. N. Hounkonnou and Fortuné Massamba, Moyal Algebra : relevant properties, projective limits and applications in non-commutative field theory, Science University Tokyo (SUT) Journal of Mathematics, 44 (2008), No. 1, 55-88
  • Fortuné Massamba, Totally Contact Umbilical Lightlike Hypersurfaces of Indefinite Sasakian Manifolds, Kodai Mathematical Journal, 31 (2008), 338-358
  • Fortuné Massamba, η-totally umbilical lightlike hypersurfaces of indefinite Sasakian manifolds, Contemporary problems in mathematical physics, Int. Chair Math. Phys. Appl. (ICMPA-UNESCO Chairs), Cotonou, 2008, 269-279
  • Fortuné Massamba, Semi-parallel lightlike hypersurfaces of indefinite Sasakian manifolds, International Journal of Contemporary Mathematical Sciences, 3 (2008), No. 13, 629-634
  • Fortuné Massamba, Lightlike hypersurfaces of indefinite Sasakian manifolds with parallel symmetric bilinear forms, Differential Geometry- Dynamical Systems, 10 (2008), 226-234
  • Fortuné Massamba, Killing and geodesic lightlike hypersurfaces of indefinite Sasakian manifolds, Turkish Journal of Mathematics, 32 (2008), 325-347
  • Fortuné Massamba, A note on umbilical lightlike hypersurfaces of indefinite Sasakian manifolds, International Journal of Contemporary Mathematical Sciences, 2 (2007), No. 32, 1557-1568
  • N. Hounkonnou, Fortuné Massamba and J. Ben Geloun, Two-dimensional noncommutive field theory on light cone, Journal of Geometry and Symmetry Physics, 6 (2006), 38-46
  • Fortuné Massamba and G. Thompson, On a system of Seiberg-Witten equations, Journal of Geometry and Physics, 56 (2006), 643-665
  • Fortuné Massamba and G. Thompson, The universal connection and Metrics on moduli spaces, Communications in Mathematical Physics, 253 (2005), 323-335